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最小阻力功路径方程的Lei群分类及其对称性化简

M·巴克德米里 Y·阿克索依

M·巴克德米里, Y·阿克索依. 最小阻力功路径方程的Lei群分类及其对称性化简[J]. 应用数学和力学, 2010, 31(7): 868-873. doi: 10.3879/j.issn.1000-0887.2010.07.012
引用本文: M·巴克德米里, Y·阿克索依. 最小阻力功路径方程的Lei群分类及其对称性化简[J]. 应用数学和力学, 2010, 31(7): 868-873. doi: 10.3879/j.issn.1000-0887.2010.07.012
Mehmet Pakdemirli, Yigit Aksoy. Group Classification for the Path Equation Describing Minimum Drag Word and Symmetry Reductions[J]. Applied Mathematics and Mechanics, 2010, 31(7): 868-873. doi: 10.3879/j.issn.1000-0887.2010.07.012
Citation: Mehmet Pakdemirli, Yigit Aksoy. Group Classification for the Path Equation Describing Minimum Drag Word and Symmetry Reductions[J]. Applied Mathematics and Mechanics, 2010, 31(7): 868-873. doi: 10.3879/j.issn.1000-0887.2010.07.012

最小阻力功路径方程的Lei群分类及其对称性化简

doi: 10.3879/j.issn.1000-0887.2010.07.012
详细信息
  • 中图分类号: O175.1; O35

Group Classification for the Path Equation Describing Minimum Drag Word and Symmetry Reductions

  • 摘要: 重新考察虑了,最早由Pakdemirli提出的描述最小阻力功的路径方程.将Lie群理论应用于一般方程,提出了关系任意高程函数群的分类.利用对称性,确定群不变解,并利用正则坐标,降低方程的阶次.
  • [1] Pakdemirli M. The drag work minimization path for a flying object with altitude-dependent drag parameters[J].Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2009, 223(5): 1113-1116. doi: 10.1243/09544062JMES1346
    [2] Abbasbandy S, Pakdemirli M. Shivanian E. Optimum path of a flying object with exponentially decaying density medium[J]. Zeitschrift für Naturforschung A, 2009, 64(a): 431-438.
    [3] Bluman G W, Kumei S. Symmetries and Differential Equations[M]. New York: Springer-Verlag, 1989.
    [4] Stephani H. Differential Equations: Their Solution Using Symmetries[M]. New York: Cambridge University Press, 1989.
    [5] Ibragimov N H. CRC Handbook of Lie Group Analysis of Differential Equations[M]. Vol 1. Boca Raton: CRC Press, 1994.
    [6] Mahomed F M. Symmetry group classification of ordinary differential equations: survey of some results[J]. Mathematical Methods in the Applied Sciences, 2007, 30(16): 1995-2012. doi: 10.1002/mma.934
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出版历程
  • 收稿日期:  1900-01-01
  • 修回日期:  2010-04-21
  • 刊出日期:  2010-07-15

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